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Best Ukrainian Author strikes with another genius algebra...

Source: Ukrainian Mathematical Olympiad 2024. Day 2, Problem 8.5

March 20, 2024
algebra

Problem Statement

Real numbers a,b,ca, b, c are such that
a2+c−bc=b2+a−ca=c2+b−aba^2+c-bc = b^2+a-ca = c^2+b-ab
Does it follow that a=b=ca=b=c?
Proposed by Mykhailo Shtandenko
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